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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Collisional redistribution of radiation. II - The effects of degeneracy on the equations of motion for the density matrix. III - The equation of motion for the correlation function and the scattered spectrum

The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.

Burnett, K.↗
NASA NTRS1979

Formulation of coupled rotor/fuselage equations of motion

The governing equations of motion of a helicopter rotor coupled to a rigid body fuselage are derived. A consistent formulation is used to derive nonlinear periodic coefficient equations of motion which can be used to study coupled rotor/fuselage dynamics in forward flight. The methodology of rotor/fuselage coupling is clearly described and the importance of an ordering scheme in deriving consistent nonlinear equations of motion is reviewed. The final equations which are presented in partial differential form can be used to model coupled rotor/fuselage aeroelastic response or stability problems.

Warmbrodt, W.↗
NASA NTRS1979

Coupled rotor and fuselage equations of motion

The governing equations of motion of a helicopter rotor coupled to a rigid body fuselage are derived. A consistent formulation is used to derive nonlinear periodic coefficient equations of motion which are used to study coupled rotor/fuselage dynamics in forward flight. Rotor/fuselage coupling is documented and the importance of an ordering scheme in deriving nonlinear equations of motion is reviewed. The nature of the final equations and the use of multiblade coordinates are discussed.

Warmbrodt, W.↗
NASA NTRS1978

Equations of motion and two-equation turbulence model for plane or axisymmetric turbulent flows in body-oriented orthogonal curvilinear coordinates and mass-averaged dependent variables

The full Navier-Stokes time-dependent, compressible, turbulent, mean-flow equations in mass-averaged variables for plane or axisymmetric flow are presented. The equations are derived in a body-oriented, orthogonal, curvilinear coordinate system. Turbulence is modelled by a system of two equations for mass-averaged turbulent kinetic energy and dissipation rate proposed. These equations are rederived and some new features are discussed. A system of second order boundary layer equations is then derived which includes the effects of longitudinal curvature and the normal pressure gradient. The Wilcox and Chambers approach is used in considering effects of streamline curvature on turbulence phenomena in turbulent boundary layer type flows. Their two-equation turbulence model with curvature terms are rederived for the cases considered in the present report. The derived system equations serves as a basis for an investigation of problems where streamline curvature is of the order of the characteristic length in the longitudinal direction.

Sislian, J. P.↗
NASA NTRS1959

Investigation of the Stability of Very Flat Spins and Analysis of Effects of Applying various Moments Utilizing the Three Moment Equations of Motion

Based on linearized equations of motion utilizing only the three moment equations and assuming only flat-spin conditions, it appears that contemporary designs (with the moment of inertia about the wing axis I(sub Y) considerably greater than the moment of inertia about the fuselage axis I(sub X) having positive values of C(sub l, sub p) (rolling-moment coefficient due to rolling) or positive values of C(sub l, sub beta) (rolling-moment coefficient due to sideslip) will probably not have a stable spin in the flat-spin region near an angle of attack of 90 deg. If the damping in pitch in flat-spin attitudes is zero, stable flat-spin conditions may not be possible on an airplane having the mass primarily distributed along the wings. The effect of moving ailerons with the spin or the effect of applying a positive pitching moment producing recovery for contemporary fighter designs will be greatest for large negative values of C(sub n, sub beta) (yawing-moment coefficient due to sideslip). In addition, for a certain critical value of positive C(sub n, sub beta), the rolling moment applied by moving ailerons with the spin or the application of a positive pitching moment will have no effect on reducing the spin rate.

Klinar, Walter J.↗
NASA NTRS1982

Equations of motion for a flexible spacecraft-lumped parameter idealization

The equations of motion for a flexible vehicle capable of arbitrary translational and rotational motions in inertial space accompanied by small elastic deformations are derived in an unabridged form. The vehicle is idealized as consisting of a single rigid body with an ensemble of mass particles interconnected by massless elastic structure. The internal elastic restoring forces are quantified in terms of a stiffness matrix. A transformation and truncation of elastic degrees of freedom is made in the interest of numerical integration efficiency. Deformation dependent terms are partitioned into a hierarchy of significance. The final set of motion equations are brought to a fully assembled first order form suitable for direct digital implementation. A FORTRAN program implementing the equations is given and its salient features described.

Storch, Joel↗
NASA NTRS1990

Analytical and experimental study of the vibration of bonded beams with a lap joint

A theoretical model to study the flexural vibration of a bonded lap joint system is described in this paper. First, equations of motion at the joint region are derived using a differential element approach. The transverse displacements of the upper and lower beam are considered to be different. The adhesive is assumed to be linearly viscoelastic and the widely used Kelvin-Voight model is used to represent the viscoelastic behavior of the adhesive. The shear force at the interface between the adhesive and the beam is obtained from the simple bending motion equations of the two beams. The resulting equations of motion are combined with the equations of transverse vibration of the beams in the unjointed regions. These are later solved as a boundary value problem to obtain the eigenvalues and eigenvectors of the system. The model can be used to predict the natural frequencies, modal damping ratios, and mode shapes of the system for free vibration. Good agreement between numerical and experimental results was obtained for a system of graphite epoxy beams lap-jointed by an epoxy adhesive.

Rao, M. D.↗
NASA NTRS1990

Coupled rotor-body equations of motion hover flight

A set of linearized equations of motion to predict the linearized dynamic response of a single rotor helicopter in a hover trim condition to cyclic pitch control inputs is described. The equations of motion assume four fuselage degrees of freedom: lateral and longitudinal translation, roll angle, pitch angle: four rotor degrees of freedom: flapping (lateral and longitudinal tilt of the tip path plane), lagging (lateral and longitudinal displacement of the rotor plane center of mass); and dynamic inflow (harmonic components). These ten degrees of freedom correspond to a system with eighteen dynamic states. In addition to examination of the full system dynamics, the computer code supplied with this report permits the examination of various reduced order models. The code is presented in a specific form such that the dynamic response of a helicopter in flight can be investigated. With minor modifications to the code the dynamics of a rotor mounted on a flexible support can also be studied.

Curtiss, H. C., Jr.↗